The major unsolved problem of the Standard Model (SM) is the hierarchy problem. This problem could have been resolved by technicolor, supersymmetry, or compositeness, but technicolor has been ruled out, and there is an abundant lack of evidence for the latter two possibilities at low energies. Thus we may need to explore new paradigms in order to find a solution, and it may be helpful to approach this problem using a different perspective—using the language of condensed matter physics. A condensed matter system that exhibits a phase transition at zero temperature as another parameter of the system (like pressure or doping concentration) is changed, undergoes a quantum phase transition since there are only quantum fluctuations rather than the usual thermal fluctuations [1]}. Typically in such phase transitions we need to tune the parameters of the system to be close to the critical point. The Higgs sector of SM is in fact very similar to a Landau-Ginsburg model. The hierarchy problem is tantamount to the fact that in order for the Higgs VEV to be small we need to be extremely close to the critical point, and hence must fine-tune the parameters of the model. If the theory is a good description of nature up to the Planck scale, a one part in \(10^{34}\)  change of the Higgs mass term will push the theory far from its critical point. At the critical point, the Higgs mass vanishes , the correlation length diverges, and the low-energy effective theory is invariant under scale/conformal transformations. Due to the fact that the SM is weakly coupled, such a critical point is well approximated by mean-field theory, where the quantum fluctuations are small.
